A unified treatment of Hilbert–Pachpatte-type inequalities for a class of non-homogeneous kernels

Tserendorj Batbold, Laith E. Azar and Mario Krnić

Applied Mathematics and Computation, 2019, vol. 343, issue C, 167-182

Abstract: In the present paper we establish a unified treatment of Hilbert–Pachpatte-type inequalities for a class of non-homogeneous kernels. Our results are derived in both discrete and integral versions. A particular emphasis is devoted to constants and weight functions appearing on the right-hand sides of the established inequalities. As an application, we obtain inequalities with constants and weight functions expressed in terms of generalized harmonic numbers, the incomplete Beta and Gamma function, and the logarithmic integral function.

Keywords: Hilbert inequality; Hilbert–Pachpatte inequality; Hölder inequality; Jensen inequality; Gamma function (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:343:y:2019:i:c:p:167-182

DOI: 10.1016/j.amc.2018.09.047

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